Based on progress in neural architecture search algorithms, efforts have been made on developing similar approaches for Quantum Ansätz (Architecture) Search (QAS) problems. Zhang et.al [1]} adapted the DARTS algorithm [2]} from NAS for QAS, which models the distribution of different operations within a single layer with the independent category probabilistic model. The search algorithm will update the parameters in the VQC as well as the probabilistic model. However, it has been shown in NAS literature that DARTS tend to assign fast-converge architectures with high probability during sampling [3]}, [4]}. Also, the off-the-shelf probabilistic distributions for modelling the architecture space tend to have difficulties when the search space is large. Later, the same group of authors developed a neural network to evaluate the performance of parameterised quantum circuits without actually training the circuits, and incorporated this neural network into quantum architecture search [5]}. While NAS algorithms often focus on image related tasks and it has been proved through many experiments that one neural network architecture can act as a backbone feature extractor for many downstream tasks, the structures of variational quantum circuits for different problems often vary a great deal with different problems, casting some doubts on the generalisation abilities of such neural predictor based QAS algorithms. Kuo et.al [6]} proposed a deep reinforcement learning based method for tackling QAS. The reinforcement learning agent is optimised by the advantage actor-critic and proximal policy optimisation algorithms.
However, NAS algorithms based on policy gradient reinforcement learning have been shown to get easily stuck in local minimal, producing less optimal solutions [7]}, [8]}. Also, the data size for training a reinforcement learning agent will explode when the number of actions the agent can choose from is large. He et.al [9]} applied meta-learning techniques to learn good heuristics of both the architecture and the parameters. Du et al. [10]} proposed a QAS algorithm based on the one-shot neural architecture search, where all possible quantum circuits are represented by a supernet with a weight-sharing strategy and the circuits are sampled uniformly during the training stage. After finishing the training stage, all circuits in the supernet are ranked and the best performed circuit will be chosen for further optimisation. Later Linghu et.al [11]} applied similar techniques on search to a classification circuit on a physical quantum processor. Meng et.al [12]} applied Monte-Carlo tree search to ansätz optimisation for problems in quantum chemistry and condensed matter physics. However, these studies often restrict their demonstrations within one or two types of problems and small-sized systems.
